Easy peasy! You can go further with it, if you like: to work out [pmath]65^2[/pmath], you could do 25 + 15 = 40 for the hundreds (4000) and [pmath]15^2 = 225[/pmath] to get [pmath]65^2 = 4,225[/pmath] – exactly what you get from the squaring fives routine.

Why does it work?

Good question. It all comes down to algebra again. Consider [pmath](50 + x) (50 + x)[/pmath]. That multiplies out to: [pmath]2500 + 100x + x^2[/pmath] – which is exactly what the recipe works out, one step at a time!

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008.
He lives with an espresso pot and nothing to prove.